Analogue of Cosmological Particle Creation in an Ion Trap

We study phonons in a dynamical chain of ions confined by a trap with a time-dependent (axial) potential strength and demonstrate that they behave in the same way as quantum fields in an expanding or contracting Universe. Based on this analogy, we present a scheme for the detection of the analogue of cosmological particle creation which should be feasible with present day technology. In order to test the quantum nature of the particle creation mechanism and to distinguish it from classical effects such as heating, we propose to measure the two-phonon amplitude via the 2nd red sideband transition and to compare it with the one-phonon amplitude (1st red sideband).

Figure 1

Schematic of the relevant energy levels (not to scale) of one ${}^{25}\mathrm{Mg}^{+}$ ion. Shown are the ground-state hyperfine levels supplying the two internal states ($|\downarrow ⟩$ and $|\uparrow ⟩$) and the first three equidistant harmonic oscillator levels $|n⟩$, related to the harmonic axial confinement in a linear ion trap. Typically, the energy splitting of the motional levels and the Zeeman shift induced by an external magnetic field are of the same order of magnitude within 1–10 MHz, therefore much smaller than the Hyperfine splitting of 1.8 GHz, the fine structure splitting of 2750 GHz and the optical transition frequency of the order of ${10}^{15}\mathrm{Hz}$. We depict the resonant transition state sensitive detection named (d) and the relevant types of off resonant ($\approx 100\mathrm{GHz}$) two-photon stimulated Raman transitions (a),(b), and (c) described in the text.

Figure 2

Initial and final population of the motional states $|n⟩$. Left: experimentally realized thermal state with $⟨\widehat{n}⟩=0.05$. Right: simulated spectrum of the squeezed thermal state with $⟨\widehat{n}⟩=1$. The predominant population of even motional states emphasizes the nonclassical character of this state.